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ps10s08sol - = MC = 60 ⇒ Q = 120 Total profit...

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1. Question 1 (a) P = 1. Q = 500 - 10 P = 500 - 10 × 1 = 490. CS = (50 - 1) × 490 2 . profit = 490 × 1 - 500 - 490 = - 500 (b) Revenue = TC PQ = 500 + Q . Q = 500 - 10 P . P (500 - 10 P ) = 500+500 - 10 P P = 25 . 5 - 550 . 25 2 . 04. Q 500 - 10 × 2 . 04 = 479 . 6. CS (50 - 2 . 04)479 . 6 2 = 11500 . 81. Profit = 0. Yes, there is deadweight loss. 2. Question 2 (a) Q T = 150 - 3 2 P + 50 - 1 2 P = 200 - 2 P P = 100 - 1 2 Q T MR = 100 - Q T = MC = 5 Q T = 95. P = 52 . 5. Profit = 52 . 5 × 95 - 5 × 95 = 4512 . 5. Q trojan = 150 - 3 2 (52 . 5) = 71 . 25. Q westwood = 50 - 1 2 (52 . 5) = 23 . 75. CS trojan = 1 2 (100 - 52 . 5)71 . 25 = 1692 . 19. CS westwood = 1 2 (100 - 52 . 5)23 . 75 = 564 . 06. (b) (c) MR trojan = 100 - 4 3 Q trojan = 5 Q trojan = 71 . 25. MR westwood = 100 - 4 Q westwood = 5 Q westwood = 23 . 75. P = 52 . 5 , profit = 4512 . 5 CS trojan = 1692 . 19 CS westwood = 564 . 06. (d) MC = 100. 3. Question 3 (a) 300 - Q 2 - 2 Q 1 = 60 = 300 - Q 1 - 2 Q 2 . Since both firms are identical. Thus, Q 1 = Q 2 = Q . Thus, 240 = 3 Q Q = 80. Profit of each firm is (300 - 80 - 80)80 - 60 ×
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Unformatted text preview: = MC = 60 ⇒ Q = 120. Total profit is (300-120)-60 × 120 = 14400. This evenly divided between firms. (c) Its quantity and profit will be equal to the combined quantity and profit of part b. (d) Suppose the original agreement is to evenly share. Then 300-60-2 Q 2 = 60 ⇒ Q 2 = 90. Profit of firm 1 is (300-90-60)60-60 × 60 = 5400. Profit of firm 2 is (300-90-60)90-60 × 90 = 8100. (e) 300-Q 2-2 Q 1 = 60 and 30 = 300-Q 1-2 Q 2 . Thus Q 1 = 70 , Q 2 = 100. (f) Firm 2 will produce, and 30 = 300-2 Q ⇒ Q = 135. Firm 1 produce nothing. Price is P = 165. Firm 1 has incentive to cheat. 1...
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